1556
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
2 BACKGROUND
2.1
Basics of sand liquefaction analysis
A. Casagrande (1936) introduced the concept of critical state
void ratio
e
c
, stating that, upon continued shearing, sands reach
the so called critical state where they yield at constant shear
stress and volume. The shear stress attained is only a function of
e
c
, which is in turn a function of the confining effective stress
σ
c
at the criticial state (Casagrande 1975). The concept applies to
drained and undrained shear: in drained shear,
σ
c
is constant,
void ratio
e
changes to pair that
σ
c
at the critical state; in
undrained shear,
e
is constant and, therefore,
σ
c
must change to
pair
e
=
e
c
(Casagrande 1936, 1975; Castro 1975, Castro and
Poulos 1977, Poulos 1981, Poulos et al 1985, Núñez 1991).
During the undrained shear of loose sands, an intermediate
“phase transformation state” exists where the shear stress is
lower than the undrained shear strength at the critical state
s
u,c
(Castro 1975, Ishihara 1993).
The shear stress at the phase transformation state is not a
properly defined “strength” because it does not correspond to
either a peak or a final stress state. However, it is noted that it
remains fairly constant for a considerable strain span and is
therefore highly relevant for engineering computations. It will
be denoted
s
u
in this paper for practicity.
Depending on the relative density of the sand, three distinct
behaviors are observed: a) for very loose sands, the phase
transformation undrained shear strength
s
u
is very low and
equals the critical state undrained shear strength
s
u,
c
; b) for
intermediate densities, a long plateau is observed in the stress-
strain plot where
s
u
can be measured, but it may be considerably
lower than
s
u,c
; and c) for dense sands a very high
s
uc
is
observed and the plateau, if any, has a very short strain span
(see Figure 2).
2.2
Theoretical estimation of undrained shear strength
For drained shear of dilating sands, it is a common practice to
compute the peak friction angle
as the sum of the critical state
friction angle
c
and a dilatancy term
which in turn depends
on void ratio
e
and effective mean pressure
p
, or
c
p
,
e
(1)
Critical state is reached when dilatancy vanishes, a fact that can
be put by the implicit relationship
p
,
e
c
0
(2)
The most widely used expression in the form of eqn. (1) is that
of Bolton (1986) which can be put in the form
c
D
r
Q
ln
p
p
ref
R
(3)
where
,
R
, and
Q
are fit parameters and
p
ref
is a reference
pressure.
Sfriso (2009) elaborated on the meaning of parameter Q as a
crushing strength measure, suggested that it should depend on
void ratio and presented the modified expression
c
D
r
ln
p
e
2.5
p
r
p
ref
R
(4)
where
p
r
is a parameter. It has been demonstrated that eqn. (4)
better predicts the critical state void ratio for high pressure
drained shear and the critical state undrained shear strength for
high pressure undrained shear (Sfriso 2009, 2010, Sfriso and
Weber 2010).
2.3
In situ estimations of shear strength
For field conditions and earthquake loading,
s
u
depends both on
the initial void ratio
e
0
and overburden stress
p
0
acting at the
beginning of the quake. To estimate the in-situ void ratio, the
SPT is used as the standard procedure in Argentina. A trigger is
always used to release the hammer, yielding an efficiency factor
of 90% employed in the energy corrections used to compute the
normalizes SPT value (N
1
)
60
(Leoni et al 2008).
For clean sands, correlations are frequently used to estimate
various parameters after SPT results. For the undrained shear
strength
s
u
(at the phase transformation line) Núñez has been
employing the following expressions (Núñez 2010b)
s
u
D
r
4.35
3.9
D
r
p
0
'
(5)
or, in terms of the SPT blowcount
s
u
N
1
60
100
0.8 N
1
60
p
0
'
(6)
3 THE POTRERILLOS CASE STUDY
3.1
Estimation of shear strength
The silt and sand layers / pockets laying under the foundations
of Potrerillos dam have a wide range of fines content, thickness
and densities, but can be roughly split into cohesive and non-
cohesive materials.
Cohesive materials were of no concern from the point of view
of cyclic liquefaction but could form a weak layer, thus
reducing the sliding stability of the dam. the undrained static
shear strength was estimated using the common expression
s
u
0.22
p
0
'
(7)
For non-plastic silts and sands, the focus was directed to the
estimation of their undrained shear strength. The limited in-situ
values showed that (N
1
)
60
ranged from 20 to 100 for the non-
plastic lenses, with an absolute minimum of 18 (Barchiesi et al
2006). A worst case value (N
1
)
60
= 16 was adopted (Núñez
2010a, 2012) and introduced in eqn. (6) to yield
s
u
16
100
0.8
16
p
0
'
0.183
p
0
'
(8)
Comparison of eqn. (7) and eqn. (8) shows that the non-plastic
materials are weaker and therefore critical for the stability of the
dam. It must be noted that, in both cases, the vertical effective
stress
p
0
must include the effect of the self-weight of the dam.
The favourable effect of the densification of the loose silt layers
under the dam dead loading was disregarded for simplicity.
3.2
Sliding stability
Focusing only in the post-earthquake sliding stability of the
dam, simple rigid-body computations can be performed,
assuming thath the dam will slide along an horizontal plane and
that sliding resistance is provided only by the shear strength at
the plane of potential sliding and passive earth pressure of the
foundation material at the downstream toe of the dam.
The self-weight of the dam
W
d
, the weight of the foundation
soils above the potential sliding plane
W
f
and the vertical
component of the water loading
U
v
were computed to yield:
W
d
550
MN m
W
f
150
MN m
U
V
100
MN m
(9)
The total shear strength at the plane of potential sliding was
computed using eqn. (8) to be
S
u
0.183
W
d
W
f
U
v
144
MN m
(10)
